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SUBROUTINE ZTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
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* .. Scalar Arguments ..
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INTEGER INCX, K, LDA, N
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CHARACTER*1 DIAG, TRANS, UPLO
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), X( * )
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* ZTBSV solves one of the systems of equations
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* A*x = b, or A'*x = b, or conjg( A' )*x = b,
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* where b and x are n element vectors and A is an n by n unit, or
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* non-unit, upper or lower triangular band matrix, with ( k + 1 )
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* No test for singularity or near-singularity is included in this
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* routine. Such tests must be performed before calling this routine.
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* On entry, UPLO specifies whether the matrix is an upper or
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* lower triangular matrix as follows:
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* UPLO = 'U' or 'u' A is an upper triangular matrix.
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* UPLO = 'L' or 'l' A is a lower triangular matrix.
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* TRANS - CHARACTER*1.
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* On entry, TRANS specifies the equations to be solved as
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* TRANS = 'N' or 'n' A*x = b.
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* TRANS = 'T' or 't' A'*x = b.
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* TRANS = 'C' or 'c' conjg( A' )*x = b.
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* On entry, DIAG specifies whether or not A is unit
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* triangular as follows:
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* DIAG = 'U' or 'u' A is assumed to be unit triangular.
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* DIAG = 'N' or 'n' A is not assumed to be unit
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* On entry, N specifies the order of the matrix A.
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* N must be at least zero.
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* On entry with UPLO = 'U' or 'u', K specifies the number of
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* super-diagonals of the matrix A.
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* On entry with UPLO = 'L' or 'l', K specifies the number of
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* sub-diagonals of the matrix A.
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* K must satisfy 0 .le. K.
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* A - COMPLEX*16 array of DIMENSION ( LDA, n ).
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* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
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* by n part of the array A must contain the upper triangular
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* band part of the matrix of coefficients, supplied column by
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* column, with the leading diagonal of the matrix in row
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* ( k + 1 ) of the array, the first super-diagonal starting at
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* position 2 in row k, and so on. The top left k by k triangle
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* of the array A is not referenced.
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* The following program segment will transfer an upper
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* triangular band matrix from conventional full matrix storage
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* DO 10, I = MAX( 1, J - K ), J
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* A( M + I, J ) = matrix( I, J )
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* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
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* by n part of the array A must contain the lower triangular
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* band part of the matrix of coefficients, supplied column by
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* column, with the leading diagonal of the matrix in row 1 of
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* the array, the first sub-diagonal starting at position 1 in
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* row 2, and so on. The bottom right k by k triangle of the
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* array A is not referenced.
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* The following program segment will transfer a lower
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* triangular band matrix from conventional full matrix storage
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* DO 10, I = J, MIN( N, J + K )
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* A( M + I, J ) = matrix( I, J )
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* Note that when DIAG = 'U' or 'u' the elements of the array A
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* corresponding to the diagonal elements of the matrix are not
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* referenced, but are assumed to be unity.
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* On entry, LDA specifies the first dimension of A as declared
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* in the calling (sub) program. LDA must be at least
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* X - COMPLEX*16 array of dimension at least
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* ( 1 + ( n - 1 )*abs( INCX ) ).
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* Before entry, the incremented array X must contain the n
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* element right-hand side vector b. On exit, X is overwritten
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* with the solution vector x.
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* On entry, INCX specifies the increment for the elements of
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* X. INCX must not be zero.
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* Level 2 Blas routine.
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* -- Written on 22-October-1986.
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* Jack Dongarra, Argonne National Lab.
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* Jeremy Du Croz, Nag Central Office.
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* Sven Hammarling, Nag Central Office.
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* Richard Hanson, Sandia National Labs.
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PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
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* .. Local Scalars ..
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INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L
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LOGICAL NOCONJ, NOUNIT
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* .. External Functions ..
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* .. External Subroutines ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG, MAX, MIN
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* .. Executable Statements ..
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* Test the input parameters.
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IF ( .NOT.LSAME( UPLO , 'U' ).AND.
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$ .NOT.LSAME( UPLO , 'L' ) )THEN
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ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
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$ .NOT.LSAME( TRANS, 'T' ).AND.
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$ .NOT.LSAME( TRANS, 'C' ) )THEN
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ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
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$ .NOT.LSAME( DIAG , 'N' ) )THEN
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ELSE IF( N.LT.0 )THEN
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ELSE IF( K.LT.0 )THEN
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ELSE IF( LDA.LT.( K + 1 ) )THEN
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ELSE IF( INCX.EQ.0 )THEN
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CALL XERBLA( 'ZTBSV ', INFO )
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* Quick return if possible.
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NOCONJ = LSAME( TRANS, 'T' )
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NOUNIT = LSAME( DIAG , 'N' )
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* Set up the start point in X if the increment is not unity. This
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* will be ( N - 1 )*INCX too small for descending loops.
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KX = 1 - ( N - 1 )*INCX
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ELSE IF( INCX.NE.1 )THEN
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* Start the operations. In this version the elements of A are
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* accessed by sequentially with one pass through A.
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IF( LSAME( TRANS, 'N' ) )THEN
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* Form x := inv( A )*x.
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IF( LSAME( UPLO, 'U' ) )THEN
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IF( X( J ).NE.ZERO )THEN
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$ X( J ) = X( J )/A( KPLUS1, J )
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DO 10, I = J - 1, MAX( 1, J - K ), -1
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X( I ) = X( I ) - TEMP*A( L + I, J )
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KX = KX + ( N - 1 )*INCX
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IF( X( JX ).NE.ZERO )THEN
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$ X( JX ) = X( JX )/A( KPLUS1, J )
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DO 30, I = J - 1, MAX( 1, J - K ), -1
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X( IX ) = X( IX ) - TEMP*A( L + I, J )
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IF( X( J ).NE.ZERO )THEN
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$ X( J ) = X( J )/A( 1, J )
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DO 50, I = J + 1, MIN( N, J + K )
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X( I ) = X( I ) - TEMP*A( L + I, J )
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IF( X( JX ).NE.ZERO )THEN
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$ X( JX ) = X( JX )/A( 1, J )
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DO 70, I = J + 1, MIN( N, J + K )
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X( IX ) = X( IX ) - TEMP*A( L + I, J )
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* Form x := inv( A' )*x or x := inv( conjg( A') )*x.
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IF( LSAME( UPLO, 'U' ) )THEN
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DO 90, I = MAX( 1, J - K ), J - 1
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TEMP = TEMP - A( L + I, J )*X( I )
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$ TEMP = TEMP/A( KPLUS1, J )
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DO 100, I = MAX( 1, J - K ), J - 1
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TEMP = TEMP - DCONJG( A( L + I, J ) )*X( I )
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$ TEMP = TEMP/DCONJG( A( KPLUS1, J ) )
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DO 120, I = MAX( 1, J - K ), J - 1
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TEMP = TEMP - A( L + I, J )*X( IX )
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$ TEMP = TEMP/A( KPLUS1, J )
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DO 130, I = MAX( 1, J - K ), J - 1
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TEMP = TEMP - DCONJG( A( L + I, J ) )*X( IX )
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$ TEMP = TEMP/DCONJG( A( KPLUS1, J ) )
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DO 150, I = MIN( N, J + K ), J + 1, -1
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TEMP = TEMP - A( L + I, J )*X( I )
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$ TEMP = TEMP/A( 1, J )
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DO 160, I = MIN( N, J + K ), J + 1, -1
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TEMP = TEMP - DCONJG( A( L + I, J ) )*X( I )
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$ TEMP = TEMP/DCONJG( A( 1, J ) )
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KX = KX + ( N - 1 )*INCX
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DO 180, I = MIN( N, J + K ), J + 1, -1
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TEMP = TEMP - A( L + I, J )*X( IX )
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$ TEMP = TEMP/A( 1, J )
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DO 190, I = MIN( N, J + K ), J + 1, -1
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TEMP = TEMP - DCONJG( A( L + I, J ) )*X( IX )
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$ TEMP = TEMP/DCONJG( A( 1, J ) )